Paper 2014/221

Hybrid Model of Fixed and Floating Point Numbers in Secure Multiparty Computations

Toomas Krips and Jan Willemson

Abstract

This paper develops a new hybrid model of floating point numbers suitable for operations in secure multi-party computations. The basic idea is to consider the significand of the floating point number as a fixed point number and implement elementary function applications separately of the significand. This gives the greatest performance gain for the power functions (e.g. inverse and square root), with computation speeds improving up to 18 times in certain configurations. Also other functions (like exponent and Gaussian error function) allow for the corresponding optimisation. We have proposed new polynomials for approximation, and implemented and benchmarked all our algorithms on the Sharemind secure multi-party computation framework.

Note: Minor errors were corrected, also the algorithm for computing the exponential function was described in more detail.